What is the least possible solution of the following equation?

Question

2x^3 - 6x = x^2

(A) -2

(B)  -1 \frac{1}{2}

(C)  -\frac{2}{3}

(D) 0

(E) 2

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Bunuel · Accepted Answer

GMATNinja Video Solution:

https://www.youtube.com/watch?v=cmpDVLHzT3w

ArpanHere · Answer

2x^3- x^2- 6x= 0
x(2x^2- x- 6)= 0
x(2x^2- 4x+ 3x- 6)= 0
x = 0
x(x-2)(2x-3)= 0
x=-3/2, 0, 2

Answer will be (B)

vasu1104 · Answer

2x^3-x^2-6x = 0
x(2x^2-x-6) = 0
x=0 or 2x^2-x-6= 0
2x^2-4x+3x-6=0
(2x+3)(x-2)=0
x= -3/2, 2

so x=-3/2,0,2

least possible value= x= -3/2

choice B

TheAdmissionHub · Answer

2x^3-x^2-6x=0

First solution is given by factoring out  x :  x*(2x^2-x-6=0)   →   x=0

Other solutions are given by solving the remaining second degree equation.
Given a second degree equation  ax^2+bx+c=0 , the Delta formula can be used to find the solutions:  x= \frac{-b ± \sqrt{b^2-4ac} }{ 2a }

Therefore:  x= \frac{1 ± \sqrt{1 + 4*2*6}}{2*2} = \frac{1 ± \sqrt{49}}{4 }= \frac{1 ± 7}{4}

So, the 2 distinct solutions are:
 x= 2 
 x=-\frac{3}{2} , which can be written also as  x=-1\frac{1}{2}

Answer: B

SwethaReddyL · Answer

Bunuel , although i understand the solutions below, i wanna know the mistake in my approach please. Thanks in advance

2x^3 - 6x = x^2
2x^3-x^2-6x = 0
x^2(2x-1)-6x=0
(x^2-6x)(2x-1)=0
x(x-6)(2x-1)=0
x=0; x=6; x=1/2

i couldn't see the blunder

Bunuel · Answer

The mistake is here:

x^2(2x - 1) - 6x = 0

You changed it to:

(x^2 - 6x)(2x - 1) = 0

That is not valid, because -6x does not have the factor (2x - 1).

Shrutika02 · Answer

why is only -3/2 the least possible?

Bunuel · Answer

What is the least possible solution of the following equation?
2x^3 - 6x = x^2

(A) -2
(B)  -1 \frac{1}{2} 
(C)  -\frac{2}{3} 
(D) 0
(E) 2

2x^3-6x=x^2

Move all terms to one side:

2x^3-x^2-6x=0

Factor out  x :

x(2x^2-x-6)=0

Factor the quadratic:

x(2x+3)(x-2)=0

So:

x=0 ,  x=-\frac{3}{2} , or  x=2

The least possible solution is therefore  -\frac{3}{2} .

Answer: B.

What is the least possible solution of the following equation?

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What is the least possible solution of the following equation?

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